n-by-n degree grid on a sphere?There are no spherical rectangles, ’cause the four angles of a quadrilateral have to add up to more than $360^\circ$. And don’t forget: the “parallels” of latitude are not “straight”, i.e. not geodesics, the way the lines of longitude are. They’re what are known as “small circles” on the surface of the sphere.

Information about the cyclic group $C_{p^n}$, where $p$ is prime and $n\geq 2$I suppose I should have said as well that every extension of finite fields is cyclic, so that you can get the particular cyclic Galois groups you were wondering about from such extensions. And that the general question of which abelian Galois groups occur for extensions of general number fields is covered by Class Field Theory. And that there isa Local Class Field Theory describing the abelian extensions of local fields like the $p$-adic numbers and their finite extensions.